Yet Another Realization of Kerr/CFT Correspondence

The correspondence between the Kerr black hole and a boundary CFT has been conjectured recently. The conjecture has been proposed first only for the half of the CFT, namely for left movers. For right movers, the correspondence has been also found out through the suitable asymptotic boundary condition. However, the boundary conditions for these two studies are exclusive to each other. The boundary condition for left movers does not allow the symmetry of right movers, and vice versa. We propose new boundary condition which allows both of left and right movers.Comment: 6 pages, references adde

Hidden and Generalized Conformal Symmetry of Kerr-Sen Spacetimes

It is recently conjectured that generic non-extremal Kerr black hole could be holographically dual to a hidden conformal field theory in two dimensions. Moreover, it is known that there are two CFT duals (pictures) to describe the charged rotating black holes which correspond to angular momentum $J$ and electric charge $Q$ of the black hole. Furthermore these two pictures can be incorporated by the CFT duals (general picture) that are generated by $SL(2,\mathbb{Z})$ modular group. The general conformal structure can be revealed by looking at charged scalar wave equation in some appropriate values of frequency and charge. In this regard, we consider the wave equation of a charged massless scalar field in background of Kerr-Sen black hole and show in the "near region", the wave equation can be reproduced by the Casimir operator of a local $SL(2,\mathbb{R})_L \times SL(2,\mathbb{R})_R$ hidden conformal symmetry. We can find the exact agreement between macroscopic and microscopic physical quantities like entropy and absorption cross section of scalars for Kerr-Sen black hole. We then find an extension of vector fields that in turn yields an extended local family of $SL(2,\mathbb{R})_L \times SL(2,\mathbb{R})_R$ hidden conformal symmetries, parameterized by one parameter. For some special values of the parameter, we find a copy of $SL(2,\mathbb{R})$ hidden conformal algebra for the charged Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole in the strong deflection limit.Comment: 16 pages, new material and results added, extensive improvements in interpretation of results, references adde

The Central Charge of the Warped AdS^3 Black Hole

The AdS/CFT conjecture offers the possibility of a quantum description for a black hole in terms of a CFT. This has led to the study of general AdS^3 type black holes with a view to constructing an explicit toy quantum black hole model. Such a CFT description would be characterized by its central charge and the dimensions of its primary fields. Recently the expression for the central charges (C_L, C_R) of the CFT dual to the warped AdS^3 have been determined using asymptotic symmetry arguments. The central charges depend, as expected, on the warping factor. We show that topological arguments, used by Witten to constrain central charges for the BTZ black hole, can be generalized to deal with the warped AdS^3 case. Topology constrains the warped factor to be rational numbers while quasinormal modes are conjectured to give the dimensions of primary fields. We find that in the limit when warping is large or when it takes special rational values the system tends to Witten's conjectured unique CFT's with central charges that are multiples of 24.Comment: 6 pages, Latex fil

String Theory on Warped AdS_3 and Virasoro Resonances

We investigate aspects of holographic duals to time-like warped AdS_3 space-times--which include G\"odel's universe--in string theory. Using worldsheet techniques similar to those that have been applied to AdS_3 backgrounds, we are able to identify space-time symmetry algebras that act on the dual boundary theory. In particular, we always find at least one Virasoro algebra with computable central charge. Interestingly, there exists a dense set of points in the moduli space of these models in which there is actually a second commuting Virasoro algebra, typically with different central charge than the first. We analyze the supersymmetry of the backgrounds, finding related enhancements, and comment on possible interpretations of these results. We also perform an asymptotic symmetry analysis at the level of supergravity, providing additional support for the worldsheet analysis.Comment: 24 pages + appendice

Multi-Disciplinary Hands-On Desktop Learning Modules and Modern Pedagogies

Our team’s research focuses on fundamental problems in undergraduate education in terms of how to expand use of well researched, yet still “new”, teaching pedagogies of ‘sensing’ or ‘hands-on’, ‘active’ and ‘problem-based learning’ within engineering courses. It is now widely accepted that traditional lectures ARE NOT best for students – yet that is what the community almost universally does. To address this issue we are developing new Desktop Learning Modules (DLMs) that contain miniaturized processes with a uniquely expandable electronic system to contend with known sensor systems/removable cartridges, as well as, unknown expansions to the project. We have shown that miniaturized mimics of industrial-scale equipment produce process data that agree with correlations developed for large-scale equipment. We are now adapting concepts shown efficacious in a single chemical engineering course to a variety of engineering classes within civil, mechanical, bio- and electrical engineering. Some examples of new hands-on learning applications in chemical engineering include a boiler / condenser and evaporative and shell & tube heat exchangers. In bioengineering, we are developing prognostic devices for separating Prostate Cancer Tumor Cells (PCTCs) from blood, sensing for the presence of PCTCs, a thermoregulation simulated limb cartridge for studying kinematics of heat flow and heat distribution in human extremities, and immunoaffinity neuron-like ion selective electrodes. In civil engineering, the DLMs illustrate open channel flow units and a solar powered Rankine cycle is underway in mechanical engineering. We are implementing DLMs along with team learning pedagogy. In this paper we will present technical aspects surrounding development of a large number of new learning cartridges. While the assessment strategies being developed are broadly applicable we will just present one instance, with the civil engineering cartridge, of the identification of misconceptions and experimental design for assessing the impact of the DLM on learning. The assessment includes a pre- and post-test assessment to determine improvement in understanding basic concepts and persistence and/or repair of misconceptions

CFT dual of the AdS Dirichlet problem: Fluid/Gravity on cut-off surfaces

We study the gravitational Dirichlet problem in AdS spacetimes with a view to understanding the boundary CFT interpretation. We define the problem as bulk Einstein's equations with Dirichlet boundary conditions on fixed timelike cut-off hypersurface. Using the fluid/gravity correspondence, we argue that one can determine non-linear solutions to this problem in the long wavelength regime. On the boundary we find a conformal fluid with Dirichlet constitutive relations, viz., the fluid propagates on a `dynamical' background metric which depends on the local fluid velocities and temperature. This boundary fluid can be re-expressed as an emergent hypersurface fluid which is non-conformal but has the same value of the shear viscosity as the boundary fluid. The hypersurface dynamics arises as a collective effect, wherein effects of the background are transmuted into the fluid degrees of freedom. Furthermore, we demonstrate that this collective fluid is forced to be non-relativistic below a critical cut-off radius in AdS to avoid acausal sound propagation with respect to the hypersurface metric. We further go on to show how one can use this set-up to embed the recent constructions of flat spacetime duals to non-relativistic fluid dynamics into the AdS/CFT correspondence, arguing that a version of the membrane paradigm arises naturally when the boundary fluid lives on a background Galilean manifold.Comment: 71 pages, 2 figures. v2: Errors in bulk metrics dual to non-relativistic fluids (both on cut-off surface and on the boundary) have been corrected. New appendix with general results added. Fixed typos. 82 pages, 2 figure

Generalized Holographic Cosmology

We consider general black hole solutions in five-dimensional spacetime in the presence of a negative cosmological constant. We obtain a cosmological evolution via the gravity/gauge theory duality (holography) by defining appropriate boundary conditions on a four-dimensional boundary hypersurface. The standard counterterms are shown to renormalize the bare parameters of the system (the four-dimensional Newton's constant and cosmological constant). We discuss the thermodynamics of cosmological evolution and present various examples. The standard brane-world scenarios are shown to be special cases of our holographic construction.Comment: 15 pages, 5 figure

Holographic Reconstruction and Renormalization in Asymptotically Ricci-flat Spacetimes

In this work we elaborate on an extension of the AdS/CFT framework to a subclass of gravitational theories with vanishing cosmological constant. By building on earlier ideas, we construct a correspondence between Ricci-flat spacetimes admitting asymptotically hyperbolic hypersurfaces and a family of conformal field theories on a codimension two manifold at null infinity. By truncating the gravity theory to the pure gravitational sector, we find the most general spacetime asymptotics, renormalize the gravitational action, reproduce the holographic stress tensors and Ward identities of the family of CFTs and show how the asymptotics is mapped to and reconstructed from conformal field theory data. In even dimensions, the holographic Weyl anomalies identify the bulk time coordinate with the spectrum of central charges with characteristic length the bulk Planck length. Consistency with locality in the bulk time direction requires a notion of locality in this spectrum.Comment: 44 pages, 4 figures. v2: minor changes in section

Real-time correlators in warped AdS/CFT correspondence

We study real-time correlators in the warped AdS/CFT correspondence. We apply the prescription used in the usual AdS/CFT correspondence and obtain the retarded Green's functions for the scalar and vector fields in the spacelike warped and the null warped black hole backgrounds. We find that the retarded Green's functions and the cross sections are well consistent with the predictions from dual CFT. Our results not only support strongly the conjectured warped AdS/CFT correspondence, but also show that the usual relativistic AdS/CFT prescription of obtaining the real-time correlators remain effective in more general backgrounds with anisotropic conformal infinity.Comment: 27 page

Gravity in the 3+1-Split Formalism II: Self-Duality and the Emergence of the Gravitational Chern-Simons in the Boundary

We study self-duality in the context of the 3+1-split formalism of gravity with non-zero cosmological constant. Lorentzian self-dual configurations are conformally flat spacetimes and have boundary data determined by classical solutions of the three-dimensional gravitational Chern-Simons. For Euclidean self-dual configurations, the relationship between their boundary initial positions and initial velocity is also determined by the three-dimensional gravitational Chern-Simons. Our results imply that bulk self-dual configurations are holographically described by the gravitational Chern-Simons theory which can either viewed as a boundary generating functional or as a boundary effective action.Comment: 25 pages; v2: minor improvements, references adde